SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 287 



As these calculations will be rather long and the result unmanageable, we will not 

 perform the elimination exactly, but only with an approximation which takes regard 

 of the application of the results. 



In the experiments the numerical value of iab will be small the wave-length 

 large in comparison to the diameter of the jet and the numerical value of iad 

 great the coefficient of viscosity small (in all the experiments |w&|<0'24 and 

 | iad \ > 20). 



For every value of x we have 



x" 



2 B [n] 2 B+ 



The series converges rapidly for small numerical values of x, but very slowly for 

 great values. From (28) it follows that 



T' / \ _ '"- T / \ 1 . 



= x ~ 



and further, by (19), that 



i) _ EL _ 1 



n + 1 ) + 2>^iy^Tl)>+2) ' ' ' J ' 



'2 (n- 1 ) ( 



Referring to the above, by the calculation of the frictimial terms in the equation 

 for the determination of b, we will therefore put 



in T / / \ f f* 2 & 2 



= -- = J B (M) 1 + 7 -7 

 ab '\_ 2n(n+ 





For calculating J n (x) for great values of x the asymptotical expression 



., J n (x)^(2vx)->{[P n (x) + iQ(x)]e(*-^+[P n (x)^^^ . (30) 



is used, in which 



, , _ (4n a -l 2 )(4n 2 -3 2 ) (4>^-l 2 ) (4 ft 2 -3 2 ) (4n 2 - 

 1.2(8^) 2 1.2.3.4 (8a,-) 4 



and 



Q M _ (4n 2 -! 2 ) (4n 2 - 



1.2.3(8o;) 3 





A few terms of the formula (30), which is only correct when the real component 

 of x is positive, will for a great numerical value of x give an excellent approximation 

 for J B (x). By our application of the formula (30), x can be given the form aib, 



